The 73-year-old Sudanese leader arrived in the Jordanian capital Amman late on Tuesday to attend an Arab League summit.
This is despite a campaign by international organizations to have him arrested over charges of genocide.
Bashir is the subject of two arrest warrants by the International Criminal Court (ICC) for war crimes and crimes against humanity in the troubled Sudanese region of Darfur.
As he visits Jordan, Amnesty International on Wednesday urged Amman to either arrest or expel him from the country.
“As one of the signatories to the Rome Statute establishing the ICC, Jordan should arrest Omar al-Bashir and hand him over to the court,” said Lynn Maalouf, deputy director of research at the Amnesty International regional office in Beirut, Lebanon.
AI claimed after it had written to the Jordanian Foreign minister over the issue in January, Amman stated its absolute commitment to arresting Mr Bashir.
However, it is not likely that Jordan, a signatory to the instruments setting up the ICC would honour this commitment.
Maalouf warned that failure to arrest Bashir would be a serious violation of these instruments and a betrayal of hundreds of thousands of victims of genocide, war crimes and crimes against humanity thought to have been committed in Darfur.